Apentix/AP Calculus AB/Unit 3: Differentiation: Composite, Implicit, and Inverse Functions/Question
AP Calculus ABmediummcq1 pt

If f(x)=x2sin⁡(2x)f(x)=x^2\sin(2x), then f′(x)=f'(x)=

A.2xcos⁡(2x)2x\cos(2x)
B.2xsin⁡(2x)−2x2cos⁡(2x)2x\sin(2x)-2x^2\cos(2x)
C.2xsin⁡(2x)+2x2cos⁡(2x)2x\sin(2x)+2x^2\cos(2x)
D.2xsin⁡(2x)+x2cos⁡(2x)2x\sin(2x)+x^2\cos(2x)

Explanation

Core Concept

Use the product rule, and apply the chain rule to the second factor. The result is 2xsin⁡(2x)+x2⋅2cos⁡(2x)2x\sin(2x)+x^2\cdot 2\cos(2x).

Correct Answer

C2xsin⁡(2x)+2x2cos⁡(2x)2x\sin(2x)+2x^2\cos(2x)

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